On the use of binary decision diagrams for solving problems on simple games

Simple games are yes/no cooperative games which arise in many practical applications. Recently, we have used reduced ordered binary decision diagrams and quasi-reduced ordered binary decision diagrams (abbreviated as Robdds and Qobdds, respectively) for the representation of simple games and for the computation of some power indices. In the present paper, we continue this work. We show how further important computational problems on simple games can be solved using Qobdds, viz. the identification of some key players, the computation of the desirability relation on individuals, the test whether a simple game is proper and strong, respectively, and the computation of Qobdd-representations for the sets of all minimal winning coalitions, all shift-minimal winning coalitions and all blocking coalitions, respectively. Applications of these solutions include the computation of recent power indices based on shift-minimal winning coalitions and the test for linear separability of a directed simple game.